As the site had been hacked and they have no backup of that database, I do not think it is possible for them to refund base on the information of deposit from a wallet. Think it yourself what will happen if same claim occurred by multiple person? You may think it is not possible as you are a legit users but there are a lot of people who will try to take a chance for the exploit of the site. I think for now they have no alternative to verify except the email which was on the receipt on the email.
only the owner of the coins will be able to confirm that this is his wallet on the exchange, just 1 signed message is enough from any address from which the deposit was made. Why is it so difficult to understand such simple and obvious things, especially for people with a reputation like yours? It seems that you bought these accounts or are a front man protecting the exchange.